Answer
The tension in the string was 13.1 N
Work Step by Step
The ball reaches a height 400 cm above the point where it was when the string was cut. We can find the ball's speed $v_0$ at the point where it was when the string was cut.
$v^2-v_0^2 = 2gy$
$0-v_0^2 = 2gy$
$v_0 = \sqrt{-2gy}$
$v_0 = \sqrt{-(2)(-9.80~m/s^2)(4.0~m)}$
$v_0 = 8.85~m/s$
The tension in the string an instant before the string broke is equal to the centripetal force.
$T = \frac{mv_0^2}{r}$
$T = \frac{(0.100~kg)(8.85~m/s)^2}{0.60~m}$
$T = 13.1~N$
The tension in the string was 13.1 N
